Functions $f, g : R \to R$ are defined, respectively, by $f(x) = x^2 + 3x + 1$, $g(x) = 2x - 3$, find $fof$.

$x^4 + 6x^3 + 14x^2 + 15x + 5$

The correct answer is Option (3) → $x^4 + 6x^3 + 14x^2 + 15x + 5$ ##

Given that, $f(x) = x^2 + 3x + 1, g(x) = 2x - 3$

$fof(x) = f\{f(x)\} = f(x^2 + 3x + 1)$

$= (x^2 + 3x + 1)^2 + 3(x^2 + 3x + 1) + 1$

$= x^4 + 9x^2 + 1 + 6x^3 + 6x + 2x^2 + 3x^2 + 9x + 3 + 1$

$= x^4 + 6x^3 + 14x^2 + 15x + 5$